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202 • Appendices DMC-2X00
10000 20000
20000
10000
Y
CD
B
A
X
Figure A-21 - X-Y Motion Path
The first line describes the straight line vector segment between points A and B. The next segment is a
circular arc, which starts at an angle of 180° and traverses -90°. Finally, the third line describes the
linear segment between points C and D. Note that the total length of the motion consists of the
segments:
A-B Linear 10000 units
B-C Circular
R
Δ
θ
π
2
360
= 15708
C-D Linear 10000
Total 35708 counts
In general, the length of each linear segment is
L
Xk
Y
k
k = +
22
Where Xk and Yk are the changes in X and Y positions along the linear segment. The length of the
circular arc is
LRkkk=ΔΘ2 360
π
The total travel distance is given by
DLk
k
n
=
=
∑
1
The velocity profile may be specified independently in terms of the vector velocity and acceleration.